This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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5
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0answers
116 views

A partial ordering on textbooks

After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever ...
3
votes
0answers
197 views

Online Model Theory Classes

Since "model theory" is kind of too general naming, I have encountered with lots of irrelevant results (like mathematical modelling etc.) when I searched for some videos on the special mathematical ...
1
vote
1answer
98 views

First Course in Linear algebra material request [duplicate]

I'm looking for good materials (can be on-line pdfs or books) in Linear Algebra,specifically in the part of basis, coordinates of vectors and the relationship of them and the matrix representation of ...
1
vote
1answer
3k views

What is matrix reduction to normal form PAQ?

Here is my university syllabus. I started doing math in vacation just to get a head start because I am a dunce in math. So, I began with chapter 2 - matrices - because it looked easier. I went half ...
18
votes
1answer
298 views

How 'commutative' can a non-commutative ring be?

Let $R$ be a finite non-commutative ring. Let $P(R)$ be the probability that two elements chosen uniformly at random commute with each other. Consider the value $$S=\sup_RP(R)$$ where the supremum ...
0
votes
2answers
1k views

Missing Exercises in Elementary Number Theory by Underwood Dudley.

I'm a beginner in math and I just started studying Elementary Number Theory by Dudley. So far I'm impressed, but I've noticed that the book does not include all the solutions to the exercises they ...
7
votes
2answers
323 views

Elementary Abelian $p$-Subgroups of $GL_n(\mathbb{F}_p)$

Let $p$ be a prime number. If $G$ is a finite group, an elementary abelian $p$-subgroup of $G$ of rank $r$ is any group $E\subset G$ such that $E\cong (\mathbb{Z}/p)^{\oplus r}.$ Let $\mathcal{E}_r$ ...
8
votes
1answer
282 views

Can a free group over a set be constructed this way (without equivalence classes of words)?

Denote category of monoids equipped with involution by $\textbf{invMon}$. Objects are pairs $\left(M,\iota\right)$ where $\iota$ is a map on the underlying set of $M$. Denoting $\iota$ by $x\mapsto\...
2
votes
2answers
199 views

Book recommendations for studying mathematical areas based on set theory

I am at the end of my studies with set theory, and I would like to continue in fundamental fashion, and study for example calculus based on set theory. So, I am talking about not calculus the way it ...
26
votes
2answers
643 views

Is there an exposition of complex analysis firmly separating the algebra, analysis, and topology?

Complex analysis seems to work because of the interplay between algebraic geometry over $\mathbb{C}$, and analysis and topology exploiting the fact that $\mathbb{C}/\mathbb{R}$ happens to be a ...
4
votes
1answer
87 views

Does the analog of homological algebra studying maps where, say, $d \circ d \circ d = 0$ have a name?

I don't have an application in mind or anything; I'm just curious. We can think about homological algebra as the study of endomorphisms $d$ such that $d \circ d = 0$. Most of homological algebra ...
11
votes
0answers
211 views

Reference on standard types

This question is about what I presume is a basic construction in type theory. The finite types are defined as follows: 0 is a finite type; if $\sigma, \tau$ are finite types, then so is $\sigma\...
10
votes
2answers
6k views

Is there a solution manual for Royden fourth edition?

I bought the fourth edition of Royden Real Analysis, this book is awesome and is quite different of third edition that has less excersices. I have the solution manual for the third edition. Is there ...
5
votes
2answers
139 views

Reference request, self study

I'm looking for references (books/lecture notes) for : Cardinality without choice, Scott's trick; Cardinal arithmetic without choice. Any suggestions ? Thanks in advance.
5
votes
3answers
629 views

Where can I learn about the lattice of partitions?

A set $P \subseteq \mathcal{P}(X)$ is a partition of $X$ if and only if all of the following conditions hold: $\emptyset \notin P$ For all $x,y \in P$, if $x \neq y$ then $x \cap y = \emptyset$. $\...
5
votes
1answer
126 views

Is there a mathematics field that studies the displaying of numbers?

I've read somewhere (not sure where) - that there is a dicotomy between the numbers and the symbols used for representing them, for example: We have the idea of twoness which can be represented in ...
2
votes
1answer
138 views

a gentle introduction to well posedness issues in fluid dynamics ( reference request)

I am looking for an introduction, either books, survey papers, to well posedness issues in fluid dynamic systems like the Navier Stokes, Euler equations or Stokes' equation and / or even for other ...
3
votes
3answers
535 views

Introduction to Pseudodifferential operators

I'm interested in elementary introduction to pseduodifferential operators and its application to hyperbolic PDE's. I know measure theory, Fourier analysis and some elementary(linear) hyperbolic PDE's ...
2
votes
4answers
434 views

Calculus book for people who know limits

I have the probably slightly unusual background of being quite comfortable with real numbers, functions, limits, sequences, series, etc, but having no knowledge of calculus beyond the definitions of ...
4
votes
1answer
277 views

Identically distributed and correlated systems of random variables

I have a rectangular grid of $n \times m$ lightbulbs on a torus, each situated at a grid point. That is, the lightbulbs' coordinates range from $(0,0)$ to $(n-1,m-1)$ and the lightbulb $(0,0)$ has ...
1
vote
1answer
90 views

Upper Bound of Sobolev norm by $L_2$ norm

A Paper by Madych and Potter states that if a function $f\in W_2^k(\mathbb{R})$ has evenly spaced zeroes (i.e. if $Z(f):=\{x:f(x)=0\}$, is such that $\underset{y\in\mathbb{R}}\sup dist(y,Z(f))=h<\...
7
votes
2answers
914 views

Good book for Riemann Surfaces

I am considering reading one of 'Algebraic curves and Riemann Surfaces' by Rick Miranda or 'Lectures on Riemann Surfaces' by Otto Forster. Which one of these is more advanced and comprehensive ? What ...
3
votes
0answers
228 views

Reference: Hölder regularity for linear elliptic equation, Neumann problem

I checked the Book of Gilbarg Trudinger on elliptic equations for (Hölder)-regularity results on weak solutions for elliptic pde. In particular, my equation is of the form $$\nabla \cdot (\kappa(x)\...
0
votes
1answer
304 views

Papers in algebraic topology

I am an undergraduate student, I have a decent background in algebraic topology, I have studied Munkres and Armstrong. I am planning to pursue research in algebraic topology and would like a list of ...
6
votes
1answer
98 views

A property of completely separable mad families

A family of sets $\mathcal{A}\subset[\omega]^\omega$ is called almost disjoint (a.d.) iff $\forall a,b\in\mathcal{A}(a\neq b\rightarrow |a\cap b|<\omega)$ and $\mathcal{A}$ is infinite (as such ...
5
votes
3answers
2k views

prerequisites for understanding game theory

I am from programming background but with very limited knowledge of maths. I am very much eager to learn and apply game theory to understand dynamics of International Politics and economics. But I am ...
5
votes
1answer
115 views

Is the variant direct image mathematically significant?

Preimages have the property that for an arbitrary function $f : X \rightarrow Y$ and all $B \subseteq Y$ it holds that $$f^{-1}(B^c)=[f^{-1}(B)]^c.$$ However, the analogous statement for direct ...
10
votes
3answers
1k views

Can you recommend some books on elliptic function?

I plan to study elliptic function. Can you recommend some books? What is the relationship between elliptic function and elliptic curve?Many thanks in advance!
3
votes
1answer
169 views

Graph clique problem

I'm not sure to what degree this is a graph problem, and algorithms question, or what, but I'll give the setup: I have a simple undirected graph given in the form (for example) $E=\{\{v_1,v_2\},\{v_0,...
3
votes
2answers
305 views

Interesting Problems for NonMath Majors

Sometime in the upcoming future, I will be doing a presentation as a college alumni to a bunch of undergrads from an organization I was in college. I did a dual major in mathematics and computer ...
3
votes
0answers
90 views

Are there any texts on order theory that treat it as decategorified category theory?

I read this post on nLab and now I want to learn some order theory. What are good texts that contain the above referenced topics, and are there any that are explicitly about order theory as ...
3
votes
2answers
103 views

A property of radical ideals

Let $A$ be a commutative ring with $1 \neq 0$. Theorem (Atiyah-MacDonald 1.13 (v)). Let $\mathfrak{a, b} \subseteq A$ be ideals. Then $\sqrt{\mathfrak{a + b}} = \mathfrak{\sqrt{\sqrt{a} + \sqrt{b}}}$....
1
vote
2answers
59 views

Number of abelian groups Vs Number of non-abelian groups

I would like to see a table that shows the number of non-abelian group for every order n. It is a preferable if the table contains the number of abelian groups of order n (this is not necessary though)...
1
vote
1answer
62 views

Information on “stronger form” of Dirichlet's Theorem on Arithmetic Progressions

From Wikipedia: "Stronger forms of Dirichlet's theorem state that, for any arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges." Can anyone direct me ...
2
votes
0answers
375 views

Good books on “advanced” stochastic analysis

Any good books suggestion for studding advanced features of stochastic analysis ? Thank's in advance
9
votes
1answer
617 views

Maximal ideals in polynomial rings over a field

Let $K$ be an algebraically closed field and let $k$ be a subfield of $K$ such that the field extension $K \mid k$ is algebraic. Let $B$ be the polynomial ring $K [x_1, \ldots, x_n]$ and let $A$ be ...
4
votes
1answer
367 views

The 'compactness cardinal' of a space

I'm looking for references (and a name!) for the following invariant of a topological space $X$: The least (infinite) cardinal $\kappa$ such that any open cover of $X$ has a subcover of cardinality ...
1
vote
1answer
67 views

Importance of estimating $\sigma^2$ in linear Statistical model

Statistical model for Complete Randomized design $y_{ij} = \mu + \tau_i + \epsilon_{ij}$ where, $i$ denotes treatment and $j$ denotes observation. $i=1,2,...,k\quad and \quad j=1,2,..., n_i$ $y_{...
6
votes
3answers
276 views

Questions on Fraenkel models

Halbeisen on page 172 contains a section entitled "The Second Fraenkel Model". The original paper by Fraenkel containing this model can be found here. I have several questions regarding this model and ...
4
votes
3answers
401 views

Book on lambda calculus logic and type theory

Can someone recommend me a book for self study which will cover topics of logic, lambda calculus and type theory. I know about "Computability and Logic" written by Bolos but it describe recursive ...
4
votes
1answer
663 views

Extending a function beyond the completion/closure of its domain

In analysis there are certain theorems that tell under which conditions you can continuously extend a continuous functions to the closure/completion of its domain (which actually give the same set, ...
6
votes
6answers
1k views

First Course in Linear Algebra book suggestions? [duplicate]

I'm starting maths degree this September and hoping to do some reading on Linear Algebra before I start. What are some good introductory books? Is there something that starts from the very beginning ...
4
votes
0answers
451 views

The Birman–Hilden Theorem and the Nielsen–Thurston classification

So this post is half question/half reference request, as I'm sure it's the kind of thing people would have thought about before (and indeed the question might even be trivial), but I've been unable to ...
15
votes
4answers
1k views

Good calculus exercises/problems?

I can't enroll in a university this year, so I'm studying calculus at home, but the only exercises about calculus that I find are the easy ones. Do you know a great page where I can find not only ...
9
votes
2answers
953 views

Mathematics Article Collection Books for Talented High School Students

I'm looking for some good books including mathematics articles which are appropriate for talented high school students. I'm NOT looking for puzzle or Olympiad problem books. Here are some of my ...
6
votes
1answer
355 views

Is there an introduction to probability and statistics that balances frequentist and bayesian views?

Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or ...
7
votes
2answers
888 views

Online course in representation theory or differential geometry

Are there any courses in representation theory that are available online? I'm looking for a course including videos, notes as well as assignments. I'd also be interested in a course in differential ...
3
votes
1answer
243 views

Books on computational complexity

Can anyone recommend a good book on the subjects of computability and computational complexity? What are the de facto standard texts (say, for graduate students) in this area? I've heard a thing or ...
2
votes
1answer
405 views

Green function of the Laplace-Dirichlet operator in a bounded domain

Let $\Omega \subset \mathbb{R}^d$, $d = 1,2,3$, be a bounded domain with $\partial \Omega$ smooth. Let $$A = -\Delta \colon H_0^1(\Omega) \cap H^2(\Omega) \to L^2(\Omega)$$be the Laplace-Dirichlet ...
1
vote
1answer
167 views

Ask book to deeply understand partially ordered sets

I learn little about ordering and poset before, but I think it's not enough and want to learn more about ordering and Poset. Can anyone please recommend some best books to learn about this topic. I ...